Homer Walker's Home Page

Homer F. Walker, Professor
Mathematical Sciences Department
Worcester Polytechnic Institute

Contact Information

Email	walker@wpi.edu
Telephone	508-831-6113
Fax	508-831-5824
Office	009A Stratton Hall

Mailing Address	Mathematical Sciences Department Worcester Polytechnic Institute 100 Institute Road Worcester, MA 01609-2280

Mathematical Sciences Department "Professional" Page

Course Materials

Current

MA 3457/CS 4033: Numerical Methods for Calculus and Differential Equations, B Term 2009
MA 590 (Special Topics): Numerical Methods for Nonlinear Equations and
Unconstrained Optimization, Fall 2009

Previous

Undergraduate
MA 1023: Calculus III, C Term 2009
MA 1024: Calculus IV, D Term 2009
MA 2073: Matrices and Linear Algebra II, C Term 2009
MA 1022: Calculus II - Integral Calculus, B Term 2006
MA 3257/CS 4032: Numerical Methods for Linear and Nonlinear Systems, B Term 2005
Graduate
MA 514: Numerical Linear Algebra, Spring 2006

MA 510/CS 522: Numerical Methods, Fall 2005
MA 512: Numerical Differential Equations, Spring 2005

Curriculum Vitae (PDF or PS) with a complete list of publications.

Software: NITSOL, a Fortran code for Newton-iterative solution of large-scale nonlinear systems.

Downloadable papers

Inexact Newton dogleg methods, with R. P. Pawlowski, J. P. Simonis, and J. N. Shadid, SIAM J. Numer. Anal., 46 (2008), 2112-2132.

On using approximate finite-differences in matrix-free Newton-Krylov methods, with P. N. Brown, R. Wasyk, and C. S. Woodward, SIAM J. Numer. Anal., 46 (2008), 1892-1911.

Globalization techniques for Newton-Krylov methods and applications to the fully-coupled solution of the Navier-Stokes equations, with R. P. Pawlowski, J. N. Shadid, and J. P. Simonis, SIAM Review, 48 (2006), 700-721.

Globalization techniques for Newton-Krylov methods and applications to the fully-coupled solution of the Navier-Stokes equations, with R. P. Pawlowski, J. N. Shadid, and J. P. Simonis, Report SAND2004-1777, Sandia National Laboratories, May, 2004.

On backtracking failure in Newton-GMRES methods with a demonstration for the Navier-Stokes equations, with R. S. Tuminaro and J. N. Shadid, J. Comp. Physics, 180 (2002), 549-558.

Simulating cyclic artery compression using a 3-D unsteady model with fluid-structure interactions, with D. Tang, C. Yang, S. Kobayashi, and D. N. Ku, Computers and Structures, 80 (2002), 1651-1665.

An adaptation of Krylov subspace methods to path following problems, SIAM J. Sci. Comput., 21 (2000), pp. 1191-1198.

NITSOL: a Newton iterative solver for nonlinear systems, with M. Pernice, Special Issue on Iterative Methods, SIAM J. Sci. Comput., 19 (1998), 302-318.

A new adaptive GMRES algorithm for achieving high accuracy, with M. Sosonkina, L. T. Watson, R. K. Kapania, Numer. Linear Algebra Appl., 5(1998), 275-297.

GMRES on (nearly) singular systems, with P. N. Brown, SIAM J. Matrix Anal. Appl., 18 (1997), 37-51.

An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transfer, with J. N. Shadid and R. S. Tuminaro, J. Comp. Physics, 137 (1997), 155-185.

Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms, with L. T. Watson, M. Sosonkina, R. C. Melville, and A. P. Morgan, ACM Trans. Math. Software, 23 (1997), 514-549.

Choosing the forcing terms in an inexact Newton method, with S. C. Eisenstat, Special Issue on Iterative Methods in Numerical Linear Algebra, SIAM J. Sci. Comput., 17 (1996), 16-32.

A simpler GMRES, with L. Zhou, Numer. Linear Algebra Appl., 1 (1994), 571-581.

Globally convergent inexact Newton methods, with S. C. Eisenstat, SIAM J. Optimization, 4 (1994), pp. 393-422.

Residual smoothing techniques for iterative methods, with L. Zhou, Special Section on Iterative Methods in Numerical Linear Algebra, SIAM J. Sci. Comput., 15 (1994), pp. 297-312.

Efficient high accuracy solutions with GMRES(m), with K. Turner, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 815-825.

Preconditioned iterative methods for homotopy curve tracking, with C. Desa, K. M. Irani, C. J. Ribbens, and L. T. Watson, Special Issue on Iterative Methods in Numerical Linear Algebra, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 30-46.

Experiments with conjugate gradient algorithms for homotopy curve tracking, with K. M. Irani, M. P. Kamat, C. J. Ribbens, and L. T. Watson, SIAM J. Optimization, 1 (1991), pp. 222-251.

Least-change secant updates of nonsquare matrices, with S. K. Bourji, SIAM J. Numer. Anal., 27 (1990), pp. 1263-1294.

Least-change secant update methods for underdetermined systems, with L. T. Watson, SIAM J. Numer. Anal., 27 (1990), pp. 1227-1262.

Asymptotics of solute dispersion in periodic porous media, with R. Bhattacharya and V. K. Gupta, SIAM J. Appl. Math., 49 (1989), pp. 86-98.

Implementation of the GMRES method using Householder transformations, SIAM J. Sci. Stat. Comput., 9 (1988), pp. 152-163.

Least-change sparse secant update methods with inaccurate secant conditions, with J. E. Dennis, Jr., SIAM J. Numer. Anal., 22 (1985), pp. 760-778.

Experiments with quasi-Newton methods for solving stiff ODE systems, with P. N. Brown and A. C. Hindmarsh, SIAM J. Sci. Stat. Comput., 6 (1985), 297-313.

Mixture densities, maximum likelihood, and the EM algorithm, with R. A. Redner, SIAM Review, 26 (1984), 195-239.

Convergence theorems for least-change secant update methods, with J. E. Dennis, Jr., SIAM J. Numer. Anal., 18 (1981), pp. 949-987.

The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions, with B. C. Peters, Jr., SIAM J. Appl. Math., 35 (1978), pp. 447-552.

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, with B. C. Peters, Jr., SIAM J. Appl. Math., 35 (1978), pp. 362-378.

Written by: Homer Walker (E-Mail: walker@wpi.edu)